Linearity tests under the null hypothesis of a random walk with drift

Rongguo Yan; Lingxiang Zhang

doi:10.1007/s00362-015-0659-1

Linearity tests under the null hypothesis of a random walk with drift

Rongguo Yan, Lingxiang Zhang^*

^*Corresponding author for this work

Xi'an University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper examines the linearity tests against smooth transition autoregressive models under the null hypothesis of a random walk with drift. The results show that the limiting distribution of the Wald-type statistic (Formula presented.) proposed by Teräsvirta (1994) and the (Formula presented.) statistic proposed by Harvey and Leybourne (2007) follow the standard (Formula presented.) distribution, whereas the robust (Formula presented.) statistic proposed by Harvey et al. (2008) diverges at a rate of (Formula presented.). The finite sample simulations show (Formula presented.) is oversized, and the robust (Formula presented.) test proposed by Harvey and Leybourne (2007) has better power performance despite being slightly undersized. Therefore, the robust (Formula presented.) statistic is recommended to be used as a conservative test in practical applications.

Original language	English
Pages (from-to)	407-418
Number of pages	12
Journal	Statistical Papers
Volume	57
Issue number	2
DOIs	https://doi.org/10.1007/s00362-015-0659-1
Publication status	Published - 1 Apr 2016

Keywords

Linearity
Random walk with drift
STAR

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10.1007/s00362-015-0659-1

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title = "Linearity tests under the null hypothesis of a random walk with drift",

abstract = "This paper examines the linearity tests against smooth transition autoregressive models under the null hypothesis of a random walk with drift. The results show that the limiting distribution of the Wald-type statistic (Formula presented.) proposed by Ter{\"a}svirta (1994) and the (Formula presented.) statistic proposed by Harvey and Leybourne (2007) follow the standard (Formula presented.) distribution, whereas the robust (Formula presented.) statistic proposed by Harvey et al. (2008) diverges at a rate of (Formula presented.). The finite sample simulations show (Formula presented.) is oversized, and the robust (Formula presented.) test proposed by Harvey and Leybourne (2007) has better power performance despite being slightly undersized. Therefore, the robust (Formula presented.) statistic is recommended to be used as a conservative test in practical applications.",

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AB - This paper examines the linearity tests against smooth transition autoregressive models under the null hypothesis of a random walk with drift. The results show that the limiting distribution of the Wald-type statistic (Formula presented.) proposed by Teräsvirta (1994) and the (Formula presented.) statistic proposed by Harvey and Leybourne (2007) follow the standard (Formula presented.) distribution, whereas the robust (Formula presented.) statistic proposed by Harvey et al. (2008) diverges at a rate of (Formula presented.). The finite sample simulations show (Formula presented.) is oversized, and the robust (Formula presented.) test proposed by Harvey and Leybourne (2007) has better power performance despite being slightly undersized. Therefore, the robust (Formula presented.) statistic is recommended to be used as a conservative test in practical applications.

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Linearity tests under the null hypothesis of a random walk with drift

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